Wavelength locker

ABSTRACT

Conventionally, wavelength locking and monitoring has been achieved used various components, including calibrated etalon filters, gratings, and arrays of color filters, which offer fairly bulky solutions that require complicated controls. An improved on-chip wavelength monitor comprises: a combination comb filter comprising a plurality of comb filters, each for receiving a test beams, and each comb filter including a substantially different FSR, e.g. 10× to 20× the next closest FSR. A controller dithers a phase tuning section of each comb filter to generate a maximum or minimum output in a corresponding photodetector indicative of the wavelength of the test signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims priority to U.S. patentapplication Ser. No. 15/855,242, filed Dec. 27, 2017, now allowed, whichis hereby incorporated by reference herein in its entirety.

TECHNICAL FIELD

The present invention relates to a wavelength locker, and in particularto an integrated wavelength monitor and locker for use with photonicintegrated circuits.

BACKGROUND

Accurately determining the absolute wavelength of a single mode lasersignal has many potential applications in many fields, includingspectroscopy, communication system, and wavelength tunable lasers.Conventionally, wavelength locking and monitoring has been achieved usedvarious components, including calibrated etalon filters, gratings, andarrays of color filters. Unfortunately, all of the conventional systemsoffer fairly bulky solutions that require complicated controls andassembly. Furthermore, some of these devices reflect a significantamount of light back to the light source that can potentially disturblaser sources, which further necessitates the use of bulky isolators.Conventional wavelength lockers and monitors that provide fineresolutions, e.g. 1 GHz or 10 pm of accuracy, typically require largefootprints.

An object of the present invention is to overcome the shortcomings ofthe prior art by providing an integrated wavelength locker with lowreflectivity and high resolution.

SUMMARY OF THE INVENTION

Accordingly, the present invention relates to a wavelength monitor andmeasurement system comprising:

a splitter for splitting a test signal into a plurality of test beams;

a combination comb filter comprising a plurality of comb filters, eachfor receiving a respective one of the test beams, each comb filterincluding a different FSR;

at least one photodetector for measuring output from each comb filter;

a phase tuning section for each comb filter for tuning a resonance ofeach of the plurality of comb filters; and

a controller for controlling the phase tuning section of each combfilter to generate a maximum or minimum output in the correspondingphotodetector indicative of the wavelength of the test signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in greater detail with reference to theaccompanying drawings which represent preferred embodiments thereof,wherein:

FIG. 1 is an schematic diagram of a wavelength locker/monitor inaccordance with an embodiment of the present invention;

FIG. 2 is a plot of the response vs wavelength of the combined combfilter device of FIG. 1;

FIG. 3 is a schematic diagram of an embodiment of a comb filter of thedevice of FIG. 1;

FIG. 4 is a schematic diagram of an embodiment of a comb filter of thedevice of FIG. 1;

FIG. 5A a plot of the response vs wavelength of the device of FIG. 3 forvarious phase shifts;

FIG. 5B a plot of the response vs wavelength of the device of FIG. 4 forvarious phase shifts.

DETAILED DESCRIPTION

While the present teachings are described in conjunction with variousembodiments and examples, it is not intended that the present teachingsbe limited to such embodiments. On the contrary, the present teachingsencompass various alternatives and equivalents, as will be appreciatedby those of skill in the art.

An embodiment of the present invention, relates to a novel compacton-chip wavelength locker (WLL) 1 based on integrated components todetermine absolute wavelength of incoming light from a laser source 2with minimum back reflection, high accuracy and stable temperatureperformance. The purpose of the WLL 1 is specifically to monitor andidentify, with great accuracy, the wavelength of an incoming lasersignal 7. One possible use for the WLL system 1 is to enable the lasersource 2 to be tuned by control system 3 to a very precise wavelength,since now there is a means of seeing the current wavelength of the laser2. The WLL 1 would be most suitable for different classes of tunablelasers 2, including integrated InP based photonic integrated circuits,hybrid III/V, and Silicon Photonic devices.

With reference to FIG. 1, the WLL 1 may use integrated components on adevice layer of an independent photonic integrated circuit (PIC), anexisting PIC including the laser source 2 or an independent PICconnected to a separate chip including the laser source 2. The WLL 1 maycomprise a tunable, periodic, high-fineness, combination comb filter 5in wavelength space, which may include a plurality of separate combfilters 4 ₁ to 4 _(n), each with a different free spectral range (FSR).A tap 6 may be used to tap off a small portion, e.g. less than 5%,typically 1% to 5%, of the light 7 from the laser source 2 forming atest signal 7′ to be fed to the WLL 1. A splitter 8 divides the testsignal 7′ into individual test beams 7″₁ to 7″_(n), each fortransmission to a respective one of the comb filters 4 ₁ to 4 _(n).

During operation, the control system 3 tunes each comb filter 4 ₁ to 4_(n) by dithering a phase shifter, and locking each individual test beam7″₁ to 7″_(n) to a high fineness peak or a null point of the respectivecomb filter 4 ₁ to 4 _(n). Once the comb filter 4 ₁ to 4 _(n) is locked,the value of a pre-calibrated electrical signal used to tune the combfilters 4 ₁ to 4 _(n) is used by the controller 3 to determine theabsolute wavelength of the test signal 7′.

To lock each comb filter 4 ₁ to 4 _(n), the control system 3 tunes thephase of each comb filter 4 ₁ to 4 _(n) using control signals 9 ₁ to 9_(n) to maximize or minimize a current generated in a correspondingphotodetector 11 ₁ to 11 _(n) depending on whether a null point or apeak point of the comb filter 4 ₁ to 4 _(n) is found, i.e. maximumtransmission or minimum transmission of light through the comb filter 4₁ to 4 _(n).

In the example plot illustrated in FIG. 2, three comb filters areutilized, i.e. a first comb filter 4 ₁ with a first fine FSR1, e.g. 10GHz to 40 GHz, ideally 20 GHz, an second comb filter 4 ₂ with a secondintermediate FSR2, e.g. 100 GHz to 800 GHz, ideally 400 GHz, and a thirdcomb filter 4 ₃ with a third coarse FSR3, e.g. 2000 GHz to 16000 GHz,ideally 8000 GHz. Additional comb filters with additional intermediateFSR's may be used. For this example, the WLL 1 is tuned whereby all ofthe combs align at a null point to the incoming light wavelength.Accordingly, the wavelength range of the comb filter 5 is defined as theFSR of the coarsest comb FSR3.

Based on this method and depending on the accuracy of electronics,wavelength accuracy as small as a fraction of the smallest FSR may beachieved. The fraction is as many phase levels as the electronics candetect within each a range. Hence each phase section needs to be tunedfor a full 2π. Obviously electronics with lower phase noise will be ableto detect finer phases. For instance, it is possible to achievewavelength accuracy at least 10 to 30 times, preferably 20 times, finerthan the FSR, e.g. achieving 18° phase accuracy.

In order to maximize the wavelength range of WLL 1, the illustratedembodiment uses multiple filters, e.g. 4 ₁ to 4 ₃, with different valuesof FSRs, e.g. FSR1, FSR2 and FSR3, respectively. The finest filter 4 ₁detects as many wavelength values within one FSR as phase levels, e.g.20 times in the example mentioned above. The second filter 4 ₂ mayconsequently have an FSR that is equal to or larger than fine filter 4 ₁by as much as the detectable phase levels. For the quoted example, thesecond FSR2 may be 10 to 30 times, preferably 20 times, larger than thefine FSR1, resulting in a detection wavelength range as large as 400times the wavelength resolution. This scheme may be repeated as manytime as possible with as many comb filters 4 ₁ to 4 _(n) as possible tocover the wavelength range of interest. The final WL range will be theFSR FSRn of the coarsest comb filter 4 _(n).

The controller 3 may actuate and control the combined comb filter 5continuously throughout the life of the device, i.e. analog control,utilizing some form of feedback loop. Alternatively, the controller 3may actuate and control the combined filter 5 whenever a wavelengthenquiry is made, e.g. according to a predetermined timing protocol, suchas upon start up, and/or at predetermined time periods

During use, the controller 3 may actuate and control all of the filters4 ₁ to 4 _(n) simultaneously. For example, each filter will determinethe wavelength of the test beam 7′₁-7′_(n) within the filters givenaccuracy and resolution. Then based on phase bias (electrical) readingsof each filter 4 ₁ to 4 _(n), the controller 3 calculates the precisewavelength of the test signal 7′. Alternatively, the controller 3 maytune the coarsest filter 4 _(n), e.g. FSR3, first to determine thewavelength of the test beam 7′_(n) within a first broad range, e.g. 400GHz for an FSR3 of 8000 GHz and 20 phase levels. Then, knowing the firstbroad range, the controller 3 many tune one or more intermediate filters4 ₂ to determine the wavelength of the test beam 7′2 within a secondintermediate range within the first broad range, e.g. 20 GHz for an FSR2of 400 GHz and 20 phase levels. Finally, knowing the intermediate range,the controller 3, tunes the finest filter 4 ₁ to determine thewavelength of the test beam 7′₁ to within a fine range within theintermediate range, e.g. 1 GHz for an FSR3 of 20 GHz and 20 phaselevels.

The on-chip comb filters 4 ₁ to 4 _(n) may be implemented using, interalia, unbalanced Mach-Zehnders (MZ) filter 30 (FIG. 3), and/or coiledracetrack resonators 51 (FIG. 4).

With reference to FIG. 3, a MZ filter 30, comprised of a first arm 31and a second arm 32, with an arm length imbalance, e.g. the longer armmay be 10%-90%, 20%-80%, 30%-50% longer or any suitable imbalance, and asmall loss imbalance, may provide high fineness combs 4 ₁ to 4 _(n). Thewavelength of the test signals 7″₁ to 7″_(n) may be determined at thenull or max points of the MZ filter 30. The phase of the MZ filter 30may be tuned by the control system 3 by including a phase tuning section33, e.g. a thermal phase tuner, on either of the arms 31 and 32. In anillustrated example, an FSR of 16 GHz is provided, and 16 distinct phaselevels may be identified within each FSR. Hence a wavelength resolutionof 1 GHz is achieved.

In order to actively balance the losses between each of the first andsecond arms 31 and 32, a variable optical attenuator 35 may be providein one or both of the first and second arms 31 and 32. In order to morepassively balance losses between each of the first and second arms, dueto components found in either of the first and second arms 31 and 32, abalancing element may be provided in each arm 31 and 32 of the MZ filter30. For example, a balancing element 34 may be provided on the first arm31 for tuning the loss of arm 31 by including similar components, e.g.transitions between different waveguide materials, that are found in thesecond arm 32. Moreover, a second variable optical attenuator (VOA) 36may be provided on the first arm 32 to balance the losses caused by thefirst VOA 34 in the first arm 31. The test signal 7″_(n) enters theinput port 37 from the splitter 8, and exits the output port 38 to thecorresponding photodetector 11 _(n).

The MZ filter 30 may be constructed to have minimum thermal cross talkbetween the phase tuning section 33 and the rest of the MZ waveguides 31and 32. Accordingly, the first and second arms 31 and 32 may eachinclude a coiled section, disposed as far away, e.g. >500 μm, from anyheat source, e.g. the phase tuning section 33, as possible, to minimizethe thermal gradient across each arm. The biggest advantage of MZfilters 30 is that they are not reflective by nature and hence noisolator will be needed for the integrated tunable laser 2. The type ofwaveguide, e.g. shape and/or material, on each arm may be constructed toreduce temperature sensitivity of the filter response and device backreflection. In order to have smaller temperature sensitivity, waveguideswith different properties and/or types may be used for the first andsecond arms 31 and 32 in the same MZ filter 30 that further boosts thesensitivity.

The following equation (1) may be used to calculate the FSR of each MZfilter 30, and the following equation (2) may be used to calculate thetemperature sensitivity Δλ/ΔT, i.e. change in wavelength per change intemperature for the MZ filter 30, wherein n_(g) is the group index, n₁and n₂ are the index of refraction for the first and second arms 31 and32, respectively, and L₁ and L₂ are the lengths of the first and secondarms 31 and 32, respectively.

$\begin{matrix}{{FSR} = \frac{\lambda^{2}}{n_{{g\; 1L_{1}} -}n_{g\; 2L_{2}}}} & (1) \\{\frac{{\Delta\lambda}\;}{\Delta \; T} = \frac{{\frac{\partial n_{1}}{\partial T}L_{1}} - {\frac{\partial n_{2}}{\partial T}L_{2}}}{n_{{g\; 1L_{1}} -}n_{g\; 2L_{2}}}} & (2)\end{matrix}$

Accordingly, to minimize the temperature sensitivity, the numerator ofequation (2) should be minimized, whereby the change in index withtemperature×the length of the first arm 31 should be substantially equalto the change in index with temperature×the length of the second arm 32.There are several different ways in which to balance this equation,including but not limited to, fabricating the first and second arms 31and 32 out of different materials, e.g. Silicon (Si) and Silicon Nitride(SiN). The shape, i.e. cross-section, of the first and second arms 31and 32 may also be different to provide a different change in index withtemperature, and therefore minimal temperature sensitivity. For example:one of the first and second arms 31 and 31 may comprise a rectangular orridge cross-section with first height and width dimensions, while theother arm may comprise a rectangular or ridge cross-section with atleast one of second different height and a second different width. Inanother example the cross-section of the first and second arms 31 and 32may have different shapes, e.g. one of the first and second arms 31 and32 may include a rectangular cross section (strip), while the otherincludes a ridge or rib waveguide cross-section, comprising a stepped orinverted T structure, with a slab portion and a ridge portion. Inanother possible embodiment, the light in one of the first and secondarms 31 and 32 may be rotated from the usual mode, e.g. TE, to theorthogonal mode, e.g. TM, using a first polarization rotator 39 a at thebeginning of the first arm, and then rotated back to the originalpolarization, e.g. TE, by a second polarization rotator 39 b, at the endof the first arm 31 Different modes may be used because the derivativeof n_(eff) with respect to temperature is significantly different forthe TM mode as compared to the TE mode.

In an example embodiment, a first comb filter 4 ₁ comprises an FSR₁ of16 GHz at 1545 nm, and a length L₁ of a first TE0 waveguide 31 of 27.137mm and a length L₂ of a second TM0 waveguide 32 of 38.103 mm. A secondcomb filter 4 ₂ comprises an FSR₂ of 160 GHz at 1545 nm, and a length L₁of a first TE0 waveguide 31 of 2.7137 mm and a length L₂ of a second TM0waveguide 32 of 3.8103 mm. The plot below of dλ/dT in μm/K vs Wavelengthin μm illustrates that a typical MZ filter 30 with similar first andsecond waveguides 31 and 32 has a consistently large change inwavelength per change in temperature, whereas a thermally balanced MZfilter 30 has a much smaller temperature sensitivity, especially in theC-band (1.53 μm-1.565 μm), hence it requires looser temperature control.

Alternatively, or in combination with the aforementioned thermallybalanced waveguides, in order to more accurately compensate for thermaleffects on the MZ filter 30, a plurality of temperature sensors 41, e.g.two to four, ideally three, may be used to map the temperature of theWLL 1. In order to make interpolation within the sensors 41 moreaccurate, the heat source, e.g. phase section 33, is placed outside ofthe area defined by the sensors 41, e.g. three sensors 41 define atriangle, four sensors 41 define a quadrilateral. Each temperaturesensor 41 may comprise two diodes, each with a different length in orderto make differential detection and achieve higher reading accuracy.Further accuracy is achieved by using four-point-detection scheme oneach diode. From the temperature readings of the plurality of sensors41, a temperature profile of the MZ filter 30 may be determined by thecontrol system 3. Based on the temperature profile, the control system 3may then compensate for the thermal effects by adjusting the peaks ofthe comb filters 4 ₁ to 4 _(n), i.e. the ultimate wavelength reading ofthe test signals 7″₁ to 7″_(n).

With reference to FIG. 4, a ring resonator 51 may also be used toachieve the high fineness spectral response required for the combfilters 4 ₁ to 4 _(n) in the WLL 1. Conventional ring or multi-ringresonators may be used, but the illustrated embodiment includes a coiledracetrack resonator 51, to minimize area and thermal effects. The coiledracetrack resonator 51 includes an input waveguide 52 with an input port53 and a through port 54. At least one closed loop waveguide 56 iscoupled to the input waveguide 52. An output waveguide 57 is coupled toan opposite side of the loop waveguide 56, and includes drop port 58,which is optically coupled to one of the photodetectors 11 ₁ to 11 _(n).When light of the resonant wavelength is passed through the loopwaveguide 56 from the input waveguide 52, it builds up in intensity overmultiple round-trips due to constructive interference and is output tothe output waveguide 57, which serves as a detector waveguide. Becauseonly a select few wavelengths will be at resonance within the loopwaveguide 56, the optical ring resonator 51 functions as a filter.

For resonance to take place in the ring resonator 51, the followingresonant condition must be satisfied:

λ_(m)=2πr n _(eff) /m

Wherein r is the radius of the ring resonator and n_(eff) is theeffective index of refraction of the waveguide material making up thering resonator 51.

Where λ_(m) is the resonant wavelength, and m is the mode number of thering resonator 51. Accordingly, in order for light to interfereconstructively inside the ring resonator 51, the circumference of theclosed loop 56 must be an integer multiple of the wavelength of thelight. As such, the mode number must be a positive integer for resonanceto take place. As a result, when the incident light contains multiplewavelengths, only the resonant wavelengths will be able to pass throughthe ring resonator 51 fully. As a result, when the wavelength of thetest beam 7 n″ matches the resonant wavelength of the ring resonator 51,a maximum transmission measurement will be detected by the photodetector11 n, whereby the value of a pre-calibrated electrical signal used totune the ring resonator 51 is used by the controller 3 to determine theabsolute wavelength of the test signal 7″_(n).

Similar to the MZ filter 20 above, the ring resonator 51 includes atleast one phase tuning section 61, e.g. thermo-optic or electro-optic,within the closed loop 56 to enable the aforementioned tunability. Thephase tuning section 61 also should include waveguides with low backreflection and small thermal coefficient. The ring resonator 51 may alsobe comprised of waveguides 52, 56 and 57 that result in minimal thermaleffects. For example: if combination of positive and negative thermalcoefficient waveguides are used. One advantage of the ring resonatordevices 51 over the MZ filter 20 based devices is that the resonatordevice 51 may be accessed both via the through port 54 and the drop port58, which provides different signal amplitudes at high fineness section.For example, providing the photodetector 11 _(n) or an additionalphotodetector optically coupled to the through port 54 may provide anindication of when light from the test signal 7″_(n) at the resonantwavelength of the ring resonator 51 is minimized or null at the throughport 54, and therefore fully passed to the drop port 58. Accordingly,the through port 54 may provide an alternative location for thephotodetector 11 _(n) or a secondary location for an additionalphotodetector providing a secondary or confirmation measurement that thering resonator 51 is locked to the wavelength of the laser signal 7.

As mentioned above with reference to the MZ filter 20, the ringresonator device 51 may also be temperature sensitive. Despiteconstructing the waveguides 52, 56 and 57, of materials to minimizethermal effects, the absolute wavelength of the high fineness point mayslightly change with temperature, resulting in reading error.Accordingly, as with the MZ filter 20, a few on-chip temperature sensingdevices 62 may be used around each ring resonator 51 to closely monitorand control its temperature. The polygon formed by temperature sensingdevices 62 should contain no heat sources to allow for thermalinterpolation anywhere inside such shape. Each temperature sensor 62 maycomprise two diodes, each with a different length in order to makedifferential detection and achieve higher reading accuracy. Furtheraccuracy is achieved by using four-point-detection scheme on each diode.From the temperature readings of the plurality of sensors 62, atemperature profile of the ring resonator filter 51 may be determined bythe control system 3. Based on the temperature profile, the controlsystem 3 may then compensate for the thermal effects by adjusting thepeaks of the comb filters 4 ₁ to 4 _(n), i.e. the ultimate wavelengthreading of the test signals 7″₁ to 7″_(n).

Each filter device, e.g. MZ filter 30 or ring resonator 51, requirescalibration to define the precise location of comb filter linesdepending on the measured temperatures, as well as the applied currentto the phase tuning section 33 or 61. This calibration data is used tocalculate the absolute wavelength based on the phase shifter bias andtemperature for which the filter, e.g. MZ filter 30 or ring resonator51, is locked to the test signal 7″₁ to 7″_(n).

FIG. 5A is an example of a fine comb filter response for different phaseshifts based on the MZ filter 40, and FIG. 5B is an example of a finecomb filter response for different phase shifts based on the coiledracetrack resonator 51. As the phase tuning section 33 or 61 is adjustedby the controller 3, the null point (or peak point) of the responseshifts. The control system 3 determines the wavelength of the testsignal 7′, and may lock the WLL 1 to either peak or null points on bothdesigns. The control system 3 may then send laser control signals backto the laser source 2 to provide adjustments to the wavelength, i.e.control the wavelength of the tunable laser 2.

The foregoing description of one or more embodiments of the inventionhas been presented for the purposes of illustration and description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed. Many modifications and variations are possiblein light of the above teaching. It is intended that the scope of theinvention be limited not by this detailed description, but rather by theclaims appended hereto.

We claim:
 1. An apparatus, comprising a laser source to generate a lasersignal and a wavelength monitor, wherein the wavelength monitorcomprises: a tap for tapping a portion of the laser signal from thelaser source to form a test signal; a splitter for splitting the testsignal into a plurality of test beams; a combination comb filtercomprising a plurality of comb filters, each one of the plurality ofcomb filters connected to receive a respective one of the test beams,each comb filter having a different FSR; a plurality of photodetectors,each one of the photodetectors configured for measuring light outputfrom a respective one of the plurality of comb filters; a plurality ofphase tuning sections, each of the plurality of phase tuning sectionsfor tuning a corresponding one of the comb filters; and a controller tocontrol the plurality of phase tuning sections to determine a wavelengthof the test signal by generating a maximum output or a minimum output insome of the plurality of photodetectors, and configured to tune thelaser source based on the determined wavelength of the test signal. 2.The apparatus according to claim 1, wherein the controller is configuredto determine the wavelength of the test signal based on values ofpre-calibration values of electrical signals for controlling the some ofthe phase tuning sections to tune corresponding ones of the plurality ofcomb filters.
 3. The apparatus according to claim 2, wherein thecontroller is configured to dither the some of the plurality of phasetuning sections such that some of the test beams are locked to a peak ora null point of the corresponding ones of the plurality of comb filters.4. The apparatus according to claim 1, wherein the plurality of combfilters comprises at least a first of the comb filters and a second ofthe comb filters; and wherein the FSR of the second of the comb filtersis at least 10 times larger than the FSR of the first of the combfilters.
 5. The apparatus according to claim 4, wherein the plurality ofcomb filters further comprises a third of the comb filters; wherein theFSR of the third of the comb filters is at least 10 times larger thanthe FSR of the second of the comb filters.
 6. The apparatus according toclaim 5, wherein the FSR of the first of the comb filters is between 10GHz to 40 GHz; wherein the FSR of the second of the comb filters isbetween 100 GHz to 800 GHz; and wherein the FSR of the third of the combfilters is between 2000 GHz to 16000 GHz.
 7. The wavelength monitoraccording to claim 5, wherein each of the plurality of phase tuningsections are configured to provide wavelength accuracy of at least 10 to30 times finer than the first FSR, the second FSR and the third FSR. 8.The apparatus according to claim 1, wherein each one of the plurality ofcomb filters comprises a ring resonator.
 9. The apparatus according toclaim 8, wherein at least one of the ring resonators compriseswaveguides with positive and negative thermal coefficients on each sidethereof to minimize temperature sensitivity between each side.
 10. Theapparatus according to claim 8, wherein each ring resonator comprises adrop port and a through port; and wherein one of the plurality ofphotodetectors is coupled to each drop port.
 11. The apparatus accordingto claim 1, wherein each of the plurality of comb filters comprises aMach-Zehnder filter.
 12. The apparatus according to claim 11, wherein atleast one of the Mach-Zehnder filters comprises a first arm and a secondarm; and wherein the first arm includes a first polarization rotator forrotating a polarization of light in the first arm, and a secondpolarization rotator for rotating back the polarization of light in thefirst arm.
 13. The apparatus according to claim 12, wherein the firstarm comprises Silicon and the second arm comprises Silicon Nitride. 14.The apparatus according to claim 12, wherein the first arm comprises astrip waveguide, and the second arm comprises a rib waveguide.
 15. Theapparatus according to claim 12, wherein the first arm includes a widththat is different than a width of the second arm.
 16. The apparatusaccording to claim 1, further comprising a temperature sensor; whereinthe temperature sensor comprises at least three temperature sensors; andwherein a heat source is placed outside an area defined by the at leastthree sensors.
 17. The apparatus according to claim 16, wherein each ofthe at least three temperature sensors comprises two diodes withdifferent lengths.